Afrouzi, G. A.; Vahidi, J.; Rasouli, S. H. On critical exponent for existence of positive solutions for some semipositone problems involving the weight function. (English) Zbl 1175.35064 Int. J. Math. Anal., Ruse 2, No. 17-20, 987-991 (2008). Summary: We study existence of positive solution for the semipositone problem of the form\[ -\Delta u=\lambda m(x)u^\alpha-c, \quad x\in\Omega, \qquad u(x)=0, \quad x\in\partial\Omega, \]where \(\Delta\) denote the Laplacian operator, \(\Omega\) is a smooth bounded domain in \(\mathbb R^N\) with \(\partial\Omega\) of class \(C^2\), \(\lambda\), \(c\) are positive parameters and the weight \(m(x)\) satisfying \(m(x)\in C(\Omega)\) and \(m(x)\geq m_0> 0\) for \(x\in\Omega\). A critical exponent is obtained for existence of positive solution by applying the method of sub-super solution. Cited in 2 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations 35B33 Critical exponents in context of PDEs Keywords:semipositone problem; positive solutions; method of sub-super solution PDFBibTeX XMLCite \textit{G. A. Afrouzi} et al., Int. J. Math. Anal., Ruse 2, No. 17--20, 987--991 (2008; Zbl 1175.35064) Full Text: Link